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Is there a generic way to refer to the summed values in this equation:

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I wanna say something like 'the result is the sum of three individual XXX XXX XXX performed on the percentile values', where XXX could be 'transformation' or 'mutations' or......and the percentile values are being represented by the P(XX) sections. What's being done, specifically, is taking the inverse of the percentile in one case, and the inverse of 1-the percentile in the two other cases. This slight difference would make the full explanation too wordy, but a short catch all phrase to use for these three terms escapes me.

Plutoro
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traggatmot
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1 Answers1

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It looks to me like you're taking a weighted sum, or linear combination (with weights $w_{pc},w_{ed},w_{leat}$), of reciprocals of quantities or their "complements", where the type of quantities are values of $P()$, at three different percentiles. But I'd like to be clearer about what $PC_{90},ED_{90},LEAT_{90}$ are. These would be values of different variates at their 90th percentile? And what is $P$, then? Recall that if you have a probability density function $f(x)=\mathbb{P}\{X=x\}$, it tells you the probability that a random variate $X$ is equal to a specific value $x$. Now the cumulative distribution $F(x)=\mathbb{P}\{X\le x\}$ gives the probability that $X$ is less than or equal to a particular value of $x$. And the 90th percentile of $X$ is $X_{90}=F^{-1}(.9)$. It looks to me like you're formula is comparing where the 90th percentile of three variates, PC, ED & LEAT, lie on another scale, by a function $P=F^{-1}$ for some other variate $X$, and then it's weighing the reciprocal of those three points (two of which are "complemented", which would make me assume that $X$ takes values in $[0,1]$ so that $F,P:[0,1]\to[0,1]$ are one-dimensional inverse copulas.

bgins
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